Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch

Wednesday, August 19, 2009

What is the most interesting number ?

What are the most interesting numbers- I allow reals and complex numbers
this time.
To avoid having too many numbers I have restricted it to
numbers that have had entire books written about them (there is one exception
that I note below), and to be of mathematical interest (e.g., the speed of light
is not included and the square root of 2, which I did include, perhaps shouldn't have been).

Review of books on 0,1,pi, e:
here,
Review of a book on i:
here.
Review of a book on square root of 2:
here.
Review of a book on phi:
here.
Review of a book on gamma (whats gamma?):
here.
If there is some mathematical constant that has had a book on it that I
have not included, please comment.

Here is my choice ranked in order of how important they are.

0. Addition is more basic then multiplication so the additive
identity comes before the multiplicative identity.

1. Multiplicative identity.

-1. Negative numbers--- what would we do without them?
One could even argue that subtraction is more important than
multiplication and make this number 2 on the list.
There is no book on -1 that I know of, but it is still too important
to not put on this list.

pi. Without pi we wouldn't have circles!

e. Ah-ha- the pi vs. e debate.
You can read about it
here or even listen to a real debate
here.
I would go with pi since the level of math it is on is more basic
then the level of math that e is on.

gamma. What is this constant? It is the difference in the limit between
natural log of n and 1 + 1/2 + ... + 1/n.
How important is it? I read the book on it pointed to above.
The book is pretty good but it mostly talks about related topics- logs,
Zeta functions, pi. So I still don't see why gamma is worth a book.
I suspect that there are more math constants that are more important that just
happened to not have books written about them. Or they have and I
don't know about them.

phi. There is the notion that the Golden Ratio pops up in math and in
nature all the time. And there are those who
disagree.

square root of 2. This is interesting historically as the first
irrational number, but I don't think it has much mathematical
significance.